Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <cstdio>
const int maxn = 200005;
int N, p[maxn], q[maxn];
bool c(int x, int y, int z) {
	if(q[x] < q[y]) return q[z] < q[x] or q[y] < q[z];
	return q[y] < q[z] and q[z] < q[x];
}
int main() {
	scanf("%d", &N);
	for(int i = 1; i <= N; ++i) scanf("%d", p + i);
	for(int i = 1; i <= N; ++i) q[p[i]] = i;
	int t = 0, f = -1;
	for(int i = N - 1; i; --i) {
		if(t == 0) {
			if(q[i] > q[i + 1]) t = 1, f = i + 1;
		} else {
			if(!c(i, i + 1, f)) t = t + 1, f = i + 1;
		}
	}
	printf("%d\n", t);
	return 0;
}